We show that long-lived bright Zeeman coherence that is responsible for absorption enhancement and steep anomalous dispersion in an atomic medium gives rise to a giant nonlinearity of the atomic susceptibility, in a similar manner to the dark coherence responsible for the well-known electromagnetically induced transparency. The intensity dependent refractive index of Cs vapour with a ground state Zeeman coherence in the vicinity of the D2 resonance line has been measured at low light intensity. The Kerr nonlinearity in the bright coherent state (n2 approx 1.0 × 10-6 cm2 mW-1) is higher than that in a dark state under the same experimental conditions. Higher order nonlinear components of the refractive index have also been estimated for both coherent states.